So, are you disregarding the definition altogether?
No, I am saying there is a problem with the definition. Currency is either fiat currency or a commodity currency. A representative currency represents either fiat currency or a commodity.
Since bitcoin represents no commodity, I conclude that it is a fiat currency. Before cryptocurrency, there was no way to create a fiat currency without a government. That doesn't mean bitcoin is not a fiat currency, but rather the ultimate in a fiat currency, since it requires no conventional government to issue it.
The defining characteristic of fiat is zero (or effectively zero) cost of production. Hence, bitcoin is not fiat. "Commodity money" is a redundancy, as any tradeable good, including money, and yes proof of hash work, is a commodity. In particular, money is an exchange commodity.